Abstract— The Slantlet Transform (SLT) is a recently developed multiresolution technique especially well-suited for piecewise linear data. The Slantlet transform is an orthogonal Discrete Wavelet Transform (DWT) with 2 zero moments and with improved time localization. It also retains the basic characteristics of the usual filterbank such as octave band characteristic and a scale dilation factor of two. However, the Slantlet transform is based on the principle of designing different filters for different scales unlike iterated filterbank approaches for the DWT. In the proposed system, Slantlet transform is implemented and used in Compression and Denoising of various input images. The performance of Slantlet Transform in terms of Compression Ratio (CR), Reconstruction Ratio (RR) and Peak-Signal-to-Noise-Ratio (PSNR) present in the reconstructed images is evaluated. Simulation results are discussed to demonstrate the effectiveness of the proposed method.

IntroductionFor many decades, scientists wanted more appropriate functions than the sines and cosines, which comprise the basis of Fourier analysis, to approximate choppy images. By their definition, these functions are non-local (and stretch out to infinity). Therefore they do a very poor job in approximating sharp spikes. Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. This makes wavelets interesting and useful. But with wavelet analy-sis, approximating functions can be used that are con-tained neatly in finite domains. Wavelets are well suited for approximating data with sharp discontinuities [1].The Discrete Wavelet transform (DWT) is usually carried out by filterbank iteration, but for a fixed number of zero moments it does not yield a discrete time basis that is optimal with respect to time localization. The Slantlet transform is an orthogonal DWT with 2 zero moments and with improved time localization. The Slantlet transform has been developed by employing the lengths of the discrete time basis function and their mo-ments as the vehicle in such a way that both time-localization and smoothness properties are achieved. Using Slantlet transform it is possible to design filters of shorter length while satisfying orthogonality and zero moments condition. The basis function retains the octave-band characteristic. Thus Slantlet transform has been used as a tool in devising an efficient method for compression and denoising of various images.

2. Literature surveyG.K. Kharate, A.A. Ghatol, et.al [2], proposed an algorithm based on decomposition of images using Dau-bechies wavelet basis. Compression of data is based on reduction of redundancy and irrelevancy. They have proposed an adaptive threshold for quantization, which is based on the type of wavelet, level of decomposition and nature of data. Sos S. Agaian, Khaled Tourshan, et.al [3] propos-es a novel approach for the parameterization of the slant-let transform with the classical slantlet and the Haar transforms are special cases of it is presented. The slantlet transform matrices are constructed first and then the filterbank is derived from them. The parametric slantlet transform performance in image and signal denoising is discussed. Panda. G, Dash. P K, et.al [4] proposes a novel approach for power quality data compression using the slantlet is presented and its performance in terms of compression ratio (CR), percentage of energy retained and mean square error present in the reconstructed image is assessed. Lakhwinder Kaur, Savita Gupta, et.al [5] pro-posed an adaptive threshold estimation method for image denoising in the wavelet domain based on the generalized Guassian distribution (GGD) modeling of subband coefficients. Lei Zhang; Bao, P; Xiaolin Wu [8] proposed a wavelet-based multiscale linear minimum mean square-error estimation (LMMSE) scheme for image denoising is proposed, and the determination of the optimal wavelet basis with respect to the proposed scheme is discussed. The overcomplete wavelet expansion (OWE), which is more effective than the orthogonal wavelet transform (OWT) in noise reduction, is used.

3.The Slantlet TransformThe Slantlet filterbank is an orthogonal filter bank for the discrete wavelet transform, where the filters are of shorter support than those of the iterated D2 filter-bank tree. This filterbank retains the desirable characteristics of the usual DWT filterbank.